This application claims benefit of Japanese Application No. 2000-254052 filed in Japan on Aug. 24, 2000, the contents of which are incorporated by this reference.
1. Field of the Invention
The present invention relates to an optical path splitting element and an image display apparatus using the same. More particularly, the present invention relates to an optical path splitting element for splitting a light beam from a single object into two optical paths. The present invention also relates to a head- or face-mounted image display apparatus using such an optical path splitting element.
2. Discussion of Related Art
There has heretofore been known an optical path splitting element for leading an image displayed by a single display device to both eyes of an observer, as disclosed in Japanese Patent Application Unexamined Publication No. [hereinafter referred to as xe2x80x9cJP(A)xe2x80x9d] 9-181999. This splitting element uses a single prism to split a light beam from the displayed image into two optical paths extending in different directions.
In an image display apparatus using the above-described splitting element, however, when the image display device is reduced in size, it is necessary to shorten the focal length of the optical system while ensuring the required eye relief. Therefore, it is difficult to construct a viewing optical system of wide field angle.
There has also been proposed an image display device using a half-mirror to split an optical path as disclosed in JP(A) 9-061748.
In the above-described conventional optical path splitting element that splits the light beam into two optical paths extending in different directions, the size of the optical path splitting element becomes unfavorably large. Accordingly, an image display apparatus using the optical path splitting element becomes undesirably large in size and heavy in weight. The above-described conventional method of splitting an optical path by using a half-mirror suffers from the problem that because the light quantity is halved for each optical path, the image for observation becomes dark.
The present invention was made in view of the above-described problems with the prior art.
Accordingly, an object of the present invention is to provide a compact optical path splitting element having a reduced number of components and also provide an image display apparatus using the optical path splitting element. More specifically, the present invention provides an optical path splitting element having at least two split axial principal rays each extending from the center of an object to the center of an image. The optical path splitting element uses a three-dimensional optical system in which bent segments forming each of the axial principal rays lie in at least two planes, thereby making the optical path splitting element compact in size. At the same time, a power is given to the optical path splitting element to reduce the number of components thereof.
To attain the above-described object, the present invention provides an optical path splitting element for splitting a light beam from a single object into two optical paths. The optical paths in the optical path splitting element are not in plane symmetry with each other but in 180-degree rotational symmetry with respect to only a straight line passing through the center of the object. The optical path splitting element has at least two pairs of reflecting surfaces in the optical paths. When a pair of reflecting surfaces closest to the object side of the optical path splitting element among the at least two pairs of reflecting surfaces are defined as a left first reflecting surface and a right first reflecting surface, respectively, and a pair of reflecting surfaces closest to the exit side of the optical path splitting element among the at least two pairs of reflecting surfaces are defined as a left final reflecting surface and a right final reflecting surface, respectively, the optical paths in the optical path splitting element are arranged so that the entering optical axis of an axial principal ray incident on the left first reflecting surface and the exiting optical axis of the axial principal ray exiting from the left final reflecting surface are not coplanar with each other, and the entering optical axis of an axial principal ray incident on the right first reflecting surface and the exiting optical axis of the axial principal ray exiting from the right final reflecting surface are not coplanar with each other. At least one pair of the at least two pairs of reflecting surfaces are formed from rotationally asymmetric curved reflecting surfaces having the function of correcting decentration aberrations.
In addition, the present invention provides an image display apparatus including an optical path splitting element for splitting a light beam from a single object into two optical paths. The optical paths in the optical path splitting element are not in plane symmetry with each other but in 180-degree rotational symmetry with respect to only a straight line passing through the center of the object. The optical path splitting element has at least two pairs of reflecting surfaces in the optical paths. When a pair of reflecting surfaces closest to the object side of the optical path splitting element among the at least two pairs of reflecting surfaces are defined as a left first reflecting surface and a right first reflecting surface, respectively, and a pair of reflecting surfaces closest to the exit side of the optical path splitting element among the at least two pairs of reflecting surfaces are defined as a left final reflecting surface and a right final reflecting surface, respectively, the optical paths in the optical path splitting element are arranged so that the entering optical axis of an axial principal ray incident on the left first reflecting surface and the exiting optical axis of the axial principal ray exiting from the left final reflecting surface are not coplanar with each other, and the entering optical axis of an axial principal ray incident on the right first reflecting surface and the exiting optical axis of the axial principal ray exiting from the right final reflecting surface are not coplanar with each other. At least one pair of the at least two pairs of reflecting surfaces are formed from rotationally asymmetric curved reflecting surfaces having the function of correcting decentration aberrations. The image display apparatus further includes an image display device placed at the position of the object. The left and right eyeballs of an observer are placed at left and right exit pupils formed in the left and right optical paths exiting the optical path splitting element, thereby allowing observation of an image displayed by the image display device.
The reasons for adopting the above-described arrangements in the present invention, together with the functions thereof, will be described below.
FIG. 1 is a perspective view schematically showing the surfaces and optical axes of a viewing optical system of an image display apparatus according to Example 1 (described later). The viewing optical system includes an optical path splitting element 10 and a pair of ocular optical systems 20L and 20R (left and right). The optical path splitting element 10 is formed from a decentered prism. The viewing optical system has a single image display device 1 common to left and right optical systems. A display light beam from the image display device 1 is split into left and right beams through the optical path splitting element 10. The beams are passed through the left and right ocular optical systems 20L and 20R to project enlarged images of the image display device 1 into the left and right eyeballs of an observer. In Example 1, the optical path splitting element 10 has a first surface 11 as a common entrance surface (refracting surface) through which left and right axial principal rays 2L and 2R emanating from the image display device 1 at an angle to each other enter the optical path splitting element 10. Regarding the left optical path, the optical path splitting element 10 has a second surface 12L, a third surface 13L, a fourth surface 14L, and a fifth surface 15L. The second surface 12L reflects the left axial principal ray 2L entering through the first surface 11. The third surface 13L reflects the left axial principal ray 2L reflected from the second surface 12L. The fourth surface 14L reflects the left axial principal ray 2L reflected from the third surface 13L. The fifth surface 15L is an exit surface (refracting surface) through which the left axial principal ray 2L reflected from the fourth surface 14L exits the optical path splitting element 10 so as to enter the left ocular optical system 20L. Regarding the right optical path, the optical path splitting element 10 has a second surface 12R, a third surface 13R, a fourth surface 14R, and a fifth surface 15R. The second surface 12R reflects the right axial principal ray 2R entering through the first surface 11. The third surface 13R reflects the right axial principal ray 2R reflected from the second surface 12R. The fourth surface 14R reflects the right axial principal ray 2R reflected from the third surface 13R. The fifth surface 15R is an exit surface (refracting surface) through which the right axial principal ray 2R reflected from the fourth surface 14R exits the optical path splitting element 10 so as to enter the right ocular optical system 20R. The left and right reflecting surfaces 12L to 14L and 12R to 14R are formed from back-coated mirrors.
The surface configurations of the above-described surfaces, i.e. from the first surface 11 to the left and right exit surfaces 15L and 15R, are determined so that the configurations of the left and right axial principal rays 2L and 2R emanating from the image display device 1 in the object plane and exiting from the left and right fifth surfaces 15L and 15R as exit surfaces are in 180-degree rotational symmetry with respect to a straight line A-Axe2x80x2 passing through the center of the display surface of the image display device 1 at approximately right angles to the display surface. To form left and right optical paths that are in 180-degree rotational symmetry with each other as stated above, the optical path splitting element 10, which is a decentered prism, should be constructed by arranging the first surface 11, the second surfaces 12R and 12L, the third surfaces 13R and 13L, the fourth surfaces 14R and 14L, and the fifth surfaces 15R and 15L so that when an optical system for the right optical path formed from the first surface 11, the second surface 12R, the third surface 13R, the fourth surface 14R and the fifth surface 15R is rotated through 180 degrees about the straight line A-Axe2x80x2, these surfaces are coincident with the first surface 11, the second surface 12L, the third surface 13L, the fourth surface 14L and the fifth surface 15L, which form an optical system for the left optical path. In this case, the axial principal ray 2R (2L) extending from the first surface 11 to the fifth surface 15R (15L) passes along a three-dimensionally decentered optical path. Therefore, it is necessary to select a surface configuration and arrangement for each surface so that the entering optical axis of the axial principal ray 2R (2L) incident on the second surface 12R (12L) as a first reflecting surface and the exiting optical axis of the axial principal ray 2R (2L) exiting from the fourth surface 14R (14L) as the final reflecting surface are not coplanar with each other.
To allow the optical path splitting element 10 to be used as a part of a viewing optical system for distributing an image displayed by the single image display device 1 to the left and right eyeballs of an observer, it is necessary to select a surface configuration and arrangement for each surface of the optical path splitting element 10 so that the left and right optical axes, which are coincident with the left and right axial principal rays 2L and 2R emerging from the left and right exit surfaces (refracting surfaces) 15L and 15R, are approximately parallel to each other so as to extend in approximately the same direction.
In the optical path splitting element 10 according to the present invention, it is desirable that at least one of the left and right reflecting surface pairs, i.e. the second surfaces 12R and 12L, the third surfaces 13R and 13L, and the fourth surfaces 14R and 14L, should be formed from rotationally asymmetric curved reflecting surfaces having the function of correcting decentration aberrations.
In the optical path splitting element 10 according to the present invention, three-dimensionally decentered optical paths are formed, as has been stated above. Consequently, the reflecting surfaces are decentered. Moreover, if an optical power is given to such a decentered reflecting surface, decentration aberrations occur. To correct the decentration aberrations, the optical path splitting element 10 needs to have at least one pair of reflecting surfaces having a rotationally asymmetric curved surface configuration.
In the present invention, a free-form surface is used as a typical example of a surface having a rotationally asymmetric curved surface configuration. A free-form surface is defined by the following equation. The Z-axis of the defining equation is the axis of a free-form surface.                     Z        =                                            cr              2                        /                          [                              1                +                                                      {                                          1                      -                                                                        (                                                      1                            +                            k                                                    )                                                ⁢                                                  c                          2                                                ⁢                                                  r                          2                                                                                      }                                                              ]                                +                                    ∑                              j                =                2                            66                        ⁢                          xe2x80x83                        ⁢                                          C                j                            ⁢                              X                m                            ⁢                              Y                n                                                                        (        a        )            
In the equation (a), the first term is a spherical surface term, and the second term is a free-form surface term.
In the spherical surface term:
c: the curvature at the vertex
k: a conic constant
r={square root over ( )}(X2+Y2)
The free-form surface term is given by                                           ∑                          j              =              2                        66                    ⁢                      xe2x80x83                    ⁢                                    C              j                        ⁢                          X              m                        ⁢                          Y              n                                      =                  xe2x80x83                ⁢                                            C              2                        ⁢            X                    +                                    C              3                        ⁢            Y                    +                                    C              4                        ⁢                          X              2                                +                                    C              5                        ⁢            XY                    +                                    C              6                        ⁢                          Y              2                                +                                    C              7                        ⁢                          X              3                                +                                                  xe2x80x83                ⁢                                            C              8                        ⁢                          X              2                        ⁢            Y                    +                                    C              9                        ⁢                          XY              2                                +                                    C              10                        ⁢                          Y              3                                +                                    C              11                        ⁢                          X              4                                +                                    C              12                        ⁢                          X              3                        ⁢            Y                    +                                                  xe2x80x83                ⁢                                            C              13                        ⁢                          X              2                        ⁢                          Y              2                                +                                    C              14                        ⁢                          XY              3                                +                                    C              15                        ⁢                          Y              4                                +                                    C              16                        ⁢                          X              5                                +                                    C              17                        ⁢                          X              4                        ⁢            Y                    +                                                  xe2x80x83                ⁢                                            C              18                        ⁢                          X              3                        ⁢                          Y              2                                +                                    C              19                        ⁢                          X              2                        ⁢                          Y              3                                +                                    C              20                        ⁢                          XY              4                                +                                    C              21                        ⁢                          Y              5                                +                                    C              22                        ⁢                          X              6                                +                                                  xe2x80x83                ⁢                                            C              23                        ⁢                          X              5                        ⁢            Y                    +                                    C              24                        ⁢                          X              4                        ⁢                          Y              2                                +                                    C              25                        ⁢                          X              3                        ⁢                          Y              3                                +                                    C              26                        ⁢                          X              2                        ⁢                          Y              4                                +                                                  xe2x80x83                ⁢                                            C              27                        ⁢                          XY              5                                +                                    C              28                        ⁢                          Y              6                                +                                    C              29                        ⁢                          X              7                                +                                    C              30                        ⁢                          X              6                        ⁢            Y                    +                                    C              31                        ⁢                          X              5                        ⁢                          Y              2                                +                                                  xe2x80x83                ⁢                                            C              32                        ⁢                          X              4                        ⁢                          Y              3                                +                                    C              33                        ⁢                          X              3                        ⁢                          Y              4                                +                                    C              34                        ⁢                          X              2                        ⁢                          Y              5                                +                                    C              35                        ⁢                          XY              6                                +                                                  xe2x80x83                ⁢                              C            36                    ⁢                      Y            7                    ⁢                      xe2x80x83                    ⁢          …                    
where Cj (j is an integer of 2 or higher) are coefficients.
In general, the above-described free-form surface does not have planes of symmetry in both the XZ- and YZ-planes. However, a free-form surface having only one plane of symmetry parallel to the YZ-plane is obtained by making all terms of odd-numbered degrees with respect to X zero. A free-form surface having only one plane of symmetry parallel to the XZ-plane is obtained by making all terms of odd-numbered degrees with respect to Y zero.
In addition, free-form surfaces as the above-described surfaces with a rotationally asymmetric curved surface configuration may be defined by Zernike polynomials. That is, the configuration of a free-form surface may be defined by the following equation (b). The Z-axis of the defining equation (b) is the axis of Zernike polynomial. A rotationally asymmetric surface is defined by polar coordinates of the height of the Z-axis with respect to the XY-plane. In the equation (b), R is the distance from the Z-axis in the XY-plane, and A is the azimuth angle about the Z-axis, which is expressed by the angle of rotation measured from the X-axis.                                                         x              =                              xe2x80x83                            ⁢                              R                xc3x97                                  cos                  ⁡                                      (                    A                    )                                                                                                                          y              =                              xe2x80x83                            ⁢                              R                xc3x97                                  sin                  ⁡                                      (                    A                    )                                                                                                                          z              =                              xe2x80x83                            ⁢                                                D                  2                                +                                                      D                    3                                    ⁢                  R                  ⁢                                      xe2x80x83                                    ⁢                                      cos                    ⁡                                          (                      A                      )                                                                      +                                                      D                    4                                    ⁢                  R                  ⁢                                      xe2x80x83                                    ⁢                                      sin                    ⁡                                          (                      A                      )                                                                      +                                                      D                    5                                    ⁢                                      R                    2                                    ⁢                                      xe2x80x83                                    ⁢                                      cos                    ⁡                                          (                                              2                        ⁢                        A                                            )                                                                      +                                                                                                        xe2x80x83                            ⁢                                                                    D                    6                                    ⁡                                      (                                                                  R                        2                                            -                      1                                        )                                                  +                                                      D                    7                                    ⁢                                                            R                      ⁢                                              xe2x80x83                                                              2                                    ⁢                                      sin                    ⁡                                          (                                              2                        ⁢                        A                                            )                                                                      +                                                                                                        xe2x80x83                            ⁢                                                                    D                    8                                    ⁢                                      R                    3                                    ⁢                                      xe2x80x83                                    ⁢                                      cos                    ⁡                                          (                                              3                        ⁢                        A                                            )                                                                      +                                                                            D                      9                                        ⁡                                          (                                                                        3                          ⁢                                                      R                            3                                                                          -                                                  2                          ⁢                          R                                                                    )                                                        ⁢                                      cos                    ⁡                                          (                      A                      )                                                                      +                                                                                                        xe2x80x83                            ⁢                                                                                          D                      10                                        ⁡                                          (                                                                        3                          ⁢                                                      R                            3                                                                          -                                                  2                          ⁢                          R                                                                    )                                                        ⁢                                      sin                    ⁡                                          (                      A                      )                                                                      +                                                      D                    11                                    ⁢                                      R                    3                                    ⁢                                      xe2x80x83                                    ⁢                                      sin                    ⁡                                          (                                              3                        ⁢                        A                                            )                                                                      +                                                      D                    12                                    ⁢                                      R                    4                                    ⁢                                      xe2x80x83                                    ⁢                                      cos                    ⁡                                          (                                              4                        ⁢                        A                                            )                                                                      +                                                                                                        xe2x80x83                            ⁢                                                                                          D                      13                                        ⁡                                          (                                                                        4                          ⁢                                                      R                            4                                                                          ⁢                                                  xe2x80x83                                                -                                                  3                          ⁢                                                      R                            2                                                                                              )                                                        ⁢                                      cos                    ⁡                                          (                                              2                        ⁢                        A                                            )                                                                      +                                                      D                    14                                    ⁡                                      (                                                                  6                        ⁢                                                  R                          4                                                                    ⁢                                              xe2x80x83                                            -                                              6                        ⁢                                                  R                          2                                                                    +                      1                                        )                                                  +                                                                                                        xe2x80x83                            ⁢                                                                                          D                      15                                        ⁡                                          (                                                                        4                          ⁢                                                      R                            4                                                                          ⁢                                                  xe2x80x83                                                -                                                  3                          ⁢                                                      R                            2                                                                                              )                                                        ⁢                                      sin                    ⁡                                          (                                              2                        ⁢                        A                                            )                                                                      +                                                      D                    16                                    ⁢                                      R                    4                                    ⁢                                      sin                    ⁡                                          (                                              4                        ⁢                        A                                            )                                                                      +                                                                                                        xe2x80x83                            ⁢                                                                    D                    17                                    ⁢                                      R                    5                                    ⁢                                      cos                    ⁡                                          (                                              5                        ⁢                        A                                            )                                                                      +                                                                            D                      18                                        ⁡                                          (                                                                        5                          ⁢                                                      R                            5                                                                          ⁢                                                  xe2x80x83                                                -                                                  4                          ⁢                                                      R                            3                                                                                              )                                                        ⁢                                      cos                    ⁡                                          (                                              3                        ⁢                        A                                            )                                                                      +                                                                                                        xe2x80x83                            ⁢                                                                                          D                      19                                        ⁡                                          (                                                                        10                          ⁢                                                      R                            5                                                                          -                                                  12                          ⁢                                                      R                            3                                                                          +                                                  3                          ⁢                          R                                                                    )                                                        ⁢                                      cos                    ⁡                                          (                      A                      )                                                                      +                                                                                                        xe2x80x83                            ⁢                                                                                          D                      20                                        ⁡                                          (                                                                        10                          ⁢                                                      R                            5                                                                          -                                                  12                          ⁢                                                      R                            3                                                                          +                                                  3                          ⁢                          R                                                                    )                                                        ⁢                                      sin                    ⁡                                          (                      A                      )                                                                      +                                                                                                        xe2x80x83                            ⁢                                                                                          D                      21                                        ⁡                                          (                                                                        5                          ⁢                                                      R                            5                                                                          -                                                  4                          ⁢                                                      R                            3                                                                                              )                                                        ⁢                                      sin                    ⁡                                          (                                              3                        ⁢                        A                                            )                                                                      +                                                      D                    22                                    ⁢                                      R                    5                                    ⁢                                      sin                    ⁡                                          (                                              5                        ⁢                        A                                            )                                                                      +                                                                                                        xe2x80x83                            ⁢                                                                    D                    23                                    ⁢                                      R                    6                                    ⁢                                      cos                    ⁡                                          (                                              6                        ⁢                        A                                            )                                                                      +                                                                            D                      24                                        ⁡                                          (                                                                        6                          ⁢                                                      R                            6                                                                          -                                                  5                          ⁢                                                      R                            4                                                                                              )                                                        ⁢                                      cos                    ⁡                                          (                                              4                        ⁢                        A                                            )                                                                      +                                                                                                        xe2x80x83                            ⁢                                                                                          D                      25                                        ⁡                                          (                                                                        15                          ⁢                                                      R                            6                                                                          -                                                  20                          ⁢                                                      R                            4                                                                          +                                                  6                          ⁢                                                      R                            2                                                                                              )                                                        ⁢                                      cos                    ⁡                                          (                                              2                        ⁢                        A                                            )                                                                      +                                                                                                        xe2x80x83                            ⁢                                                                    D                    26                                    ⁡                                      (                                                                  20                        ⁢                                                  R                          6                                                                    -                                              30                        ⁢                                                  R                          4                                                                    +                                              12                        ⁢                                                  R                          2                                                                    -                      1                                        )                                                  +                                                                                                        xe2x80x83                            ⁢                                                                                          D                      27                                        ⁡                                          (                                                                        15                          ⁢                                                      R                            6                                                                          -                                                  20                          ⁢                                                      R                            4                                                                          +                                                  6                          ⁢                                                      R                            2                                                                                              )                                                        ⁢                                      sin                    ⁡                                          (                                              2                        ⁢                        A                                            )                                                                      +                                                                                                        xe2x80x83                            ⁢                                                                                          D                      28                                        ⁡                                          (                                                                        6                          ⁢                                                      R                            6                                                                          -                                                  5                          ⁢                                                      R                            4                                                                                              )                                                        ⁢                                      sin                    ⁡                                          (                                              4                        ⁢                        A                                            )                                                                      +                                  xe2x80x83                                ⁢                                                      D                    29                                    ⁢                                      R                    6                                    ⁢                                      xe2x80x83                                    ⁢                                      sin                    ⁡                                          (                                              6                        ⁢                        A                                            )                                                        ⁢                                      xe2x80x83                                    ⁢                  …                                                                                        (        b        )            
where Dm (m is an integer of 2 or higher) are coefficients.
It should be noted that to design an optical system symmetric with respect to the X-axis direction, D4, D5, D6, D10, D11, D12, D13, D14, D20, D21, D22 . . . should be used.
The above defining equations are shown to exemplify surfaces with a rotationally asymmetric curved surface configuration. Therefore, the same advantageous effects can be obtained for any other defining equation that expresses such a rotationally asymmetric curved surface configuration.
It should be noted that other examples of defining equations for free-form surfaces include the following defining equation (c):
Z=xcexa3xcexa3CnmXY
Assuming that k=7 (polynomial of degree 7), for example, a free-form surface is expressed by an expanded form of the above equation as follows:                                                         Z              =                              xe2x80x83                            ⁢                                                C                  2                                +                                                      C                    3                                    ⁢                  Y                                +                                                      C                    4                                    ⁢                                      "LeftBracketingBar"                    X                    "RightBracketingBar"                                                  +                                                      C                    5                                    ⁢                                      Y                    2                                                  +                                                      C                    6                                    ⁢                  Y                  ⁢                                      "LeftBracketingBar"                    X                    "RightBracketingBar"                                                  +                                                      C                    7                                    ⁢                                      X                    2                                                  +                                                      C                    8                                    ⁢                                      Y                    3                                                  +                                                                                                        xe2x80x83                            ⁢                                                                    C                    9                                    ⁢                                      Y                    2                                    ⁢                                      "LeftBracketingBar"                    X                    "RightBracketingBar"                                                  +                                                      C                    10                                    ⁢                                      YX                    2                                                  +                                                      C                    11                                    ⁢                                      "LeftBracketingBar"                                          X                      3                                        "RightBracketingBar"                                                  +                                                      C                    12                                    ⁢                                      Y                    4                                                  +                                                      C                    13                                    ⁢                                      Y                    3                                    ⁢                                      "LeftBracketingBar"                    X                    "RightBracketingBar"                                                  +                                                                                                        xe2x80x83                            ⁢                                                                    C                    14                                    ⁢                                      Y                    2                                    ⁢                                      X                    2                                                  +                                                      C                    15                                    ⁢                  Y                  ⁢                                      "LeftBracketingBar"                                          X                      3                                        "RightBracketingBar"                                                  +                                                      C                    16                                    ⁢                                      X                    4                                                  +                                                      C                    17                                    ⁢                                      Y                    5                                                  +                                                      C                    18                                    ⁢                                      Y                    4                                    ⁢                                      "LeftBracketingBar"                    X                    "RightBracketingBar"                                                  +                                                                                                        xe2x80x83                            ⁢                                                                    C                    19                                    ⁢                                      Y                    3                                    ⁢                                      X                    2                                                  +                                                      C                    20                                    ⁢                                      Y                    2                                    ⁢                                      "LeftBracketingBar"                                          X                      3                                        "RightBracketingBar"                                                  +                                                      C                    21                                    ⁢                                      YX                    4                                                  +                                                      C                    22                                    ⁢                                      "LeftBracketingBar"                                          X                      5                                        "RightBracketingBar"                                                  +                                                                                                        xe2x80x83                            ⁢                                                                    C                    23                                    ⁢                                      Y                    6                                                  +                                                      C                    24                                    ⁢                                      Y                    5                                    ⁢                                      "LeftBracketingBar"                    X                    "RightBracketingBar"                                                  +                                                      C                    25                                    ⁢                                      Y                    4                                    ⁢                                      X                    2                                                  +                                                      C                    26                                    ⁢                                      Y                    3                                    ⁢                                      "LeftBracketingBar"                                          X                      3                                        "RightBracketingBar"                                                  +                                                                                                        xe2x80x83                            ⁢                                                                    C                    27                                    ⁢                                      Y                    2                                    ⁢                                      X                    4                                                  +                                                      C                    28                                    ⁢                  Y                  ⁢                                      "LeftBracketingBar"                                          X                      5                                        "RightBracketingBar"                                                  +                                                      C                    29                                    ⁢                                      X                    6                                                  +                                                      C                    30                                    ⁢                                      Y                    7                                                  +                                                      C                    31                                    ⁢                                      Y                    6                                    ⁢                                      "LeftBracketingBar"                    X                    "RightBracketingBar"                                                  +                                                                                                        xe2x80x83                            ⁢                                                                    C                    32                                    ⁢                                      Y                    5                                    ⁢                                      X                    2                                                  +                                                      C                    33                                    ⁢                                      Y                    4                                    ⁢                                      "LeftBracketingBar"                                          X                      3                                        "RightBracketingBar"                                                  +                                                      C                    34                                    ⁢                                      Y                    3                                    ⁢                                      X                    4                                                  +                                                      C                    35                                    ⁢                                      Y                    2                                    ⁢                                      "LeftBracketingBar"                                          X                      5                                        "RightBracketingBar"                                                  +                                                                                                        xe2x80x83                            ⁢                                                                    C                    36                                    ⁢                                      YX                    6                                                  +                                                      C                    37                                    ⁢                                      "LeftBracketingBar"                                          X                      7                                        "RightBracketingBar"                                                                                                          (        c        )            
It should be noted that an anamorphic surface or a toric surface is also usable as a surface having a rotationally asymmetric curved surface configuration.
It should be noted that the optical path splitting element 10 according to the present invention can have at least three pairs of reflecting surfaces for the left and right optical paths, i.e. the second surfaces 12R and 12L, the third surfaces 13R and 13L, and the fourth surfaces 14R and 14L, as in the example shown in FIG. 1. In this case, it is desirable that the at least three pairs of reflecting surfaces should be formed from rotationally asymmetric curved reflecting surfaces having the function of correcting decentration aberrations.
The above-described optical path splitting element 10 according to the present invention can be used as at least a part of a viewing optical system for distributing an image displayed by a single image display device 1 to the left and right eyeballs of an observer, as shown in FIG. 1, by way of example. In actuality, it is desirable that the left and right ocular optical systems 20L and 20R should be placed in the left and right exiting optical paths, whereby intermediate images 3L and 3R formed in the left and right optical paths (in Example 1, intermediate images 3L and 3R are formed within the prism between the fourth surfaces 14L and 14R and the fifth surfaces 15L and 15R, respectively) are viewed as enlarged images through the ocular optical systems 20L and 20R. In this case, left and right exit pupils 4L and 4R of the left and right viewing optical paths are formed at the respective exit sides of the left and right ocular optical systems 20L and 20R. Therefore, the observer""s left and right eyes are placed at the positions of the left and right exit pupils 4L and 4R to view the enlarged intermediate images 3L and 3R.
Incidentally, the surface configurations of the surfaces of the left and right optical systems, i.e. from the first surface 11 to the left and right fifth surfaces 15L and 15R, are determined so that the configurations of the left and right axial principal rays 2L and 2R emanating from the image display device 1 and exiting from the left and right fifth surfaces 15L and 15R as exit surfaces are in 180-degree rotational symmetry with respect to a straight line A-Axe2x80x2 passing through the center of the display surface of the image display device 1 at approximately right angles to the display surface, as has been stated above. Accordingly, the left optical system extending from the first surface 11 to the fifth surface 15L and the right optical system extending from the first surface 11 to the fifth surface 15R are in 180-degree rotational symmetry about the straight line A-Axe2x80x2. Moreover, the left and right optical systems are three-dimensionally decentered reflecting optical systems. Therefore, the intermediate images 3L and 3R are generally rotated through the same angle in the same direction about the respective optical axes. Accordingly, an image naturally oriented with respect to both the horizontal and vertical directions cannot be observed unless the image display device 1, which is placed in the object plane, is rotated in the opposite direction to the direction of rotation of the intermediate images 3L and 3R through the same angle as the angle of rotation about the straight line A-Axe2x80x2 as an axis of rotation so that the horizontal direction of the image display area of the image display device 1 is at an angle to a plane containing the left and right optical paths emerging from the optical path splitting element 10 (in the case of a viewing optical system for observation with two eyes, this plane is parallel to a horizontal direction connecting the centers of the pupils of the two eyes).
Incidentally, it is desirable to satisfy the following condition:
10xc2x0 less than xcex8 less than 150xc2x0xe2x80x83xe2x80x83(1)
where xcex8 is the angle formed between the axial principal rays 2L and 2R of left and right light beams led from each pixel in the center of the image display device 1 to the left and right eyes of the observer (i.e. the angle formed between the axial principal rays 2L and 2R before being incident on the first surface 11).
The condition (1) needs to be satisfied in order to separate the image light beams for the two eyes appropriately. If xcex8 is not larger than the lower limit, i.e. 10xc2x0, the effective diameter portions of the left and right optical surfaces, particularly those of the first surfaces 2L and 2R undesirably overlap each other. Accordingly, the optical system has to be increased in size in order to ensure the required effective diameter of each of the first surfaces 2L and 2R and hence becomes unsuitable for use as the optical system of a head- or face-mounted image display apparatus. Conversely, if xcex8 is not smaller than the upper limit, i.e. 150xc2x0, an image display device having very wide viewing angle characteristics is needed to serve as the image display device 1. At the same time, the solid angle of the image light beam becomes small. As a result, it becomes impossible to observe a bright image. Regarding the angle xcex8, it is preferable to satisfy the following condition:
15xc2x0 less than xcex8 less than 120xc2x0xe2x80x83xe2x80x83(1-1)
In Example 1 (described later), xcex8=41.12xc2x0. In Example 2, xcex8=32.54xc2x0.
The above-described optical path splitting element 10 is also usable to combine together rays in two optical paths by using the optical paths reversely instead of splitting an optical path from a single object as stated above.
The above-described image display apparatus can be used as an image pickup apparatus in which an image pickup device is provided in place of the image display device 1 in the above-described arrangement. In this case, the exit pupils 4L and 4R are arranged as entrance pupils through which a light beam from a subject passes, and a subject image is formed on the image pickup device.
Further, the image display apparatus can be used as a projection apparatus in which a projection object is provided in place of the image display device 1 in the foregoing arrangement. A screen is placed in front of the exit pupils 4L and 4R to form a projected image of the projection object on the screen.
Still other objects and advantages of the invention will in part be obvious and will in part be apparent from the specification.
The invention accordingly comprises the features of construction, combinations of elements, and arrangement of parts which will be exemplified in the construction hereinafter set forth, and the scope of the invention will be indicated in the claims.